If x = 2 - 2 ^ { 1 / 3 } + 2 ^ { 2 / 3 }, then find the value of x ^ { 3 } - 6 x ^ { 2 } + 18 x + 26 ?

SSC MTS Model Paper 4

Question : 49 of 150

Marks: +1, -0

x = 2 - 2 ^ { 1 / 3 } + 2 ^ { 2 / 3 }

, then find the value of

x ^ { 3 } - 6 x ^ { 2 } + 18 x + 26 ?

Solution:

Formula:

( { B } ) ^ { 3 } + 3 ( { B } ) ^ { 2 } - ( { B } ) ^ { 1 } + ( { B } ) ^ { 2 }

= B denotes base = 2

= ( 2 ) ^ { 3 } + 3 ( 2 ) ^ { 2 } - ( 2 ) ^ { 1 } + ( 2 ) ^ { 2 }

= 8 + 12 - 2 + 4 = 22 + 26

=48

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